Answer: 165 degrees
Step-by-step explanation:
Let's start off and name the angle between the hour and minute hand x, representing the number of degrees between the hands. Next, let's look at the minute hand first. After exactly an hour, the minute hand does not change its position(since after one hour, it comes back to where it was previously). As for the hour hand however, its position differs by exactly "1 hour tick", which is equivalent to 30 degrees (360 / 12 hours). What that implies is that x would have to equal x + 30, which is clearly impossible. However, we can think about the problem in a different way: by looking at the acute angle only between the hands, that would indeed be possible. Assuming that x + 30 is greater than 180(since if it wasn't, that wouldn't be possible), we can write the following equation:
x = 360 - (x+30)
, with the right hand side coming from the fact that the obtuse angle of x + 30 must have an acute counterpart, of which both add up to 360.
Then, we can simplify to:
x = 330 - x
or:
2x = 330
x = 165.
This gives us our only answer of 165 degrees
help please im so lost
Volume of given two cylinders are 115.52π m³ and 350π in³
What is the formula for the volume of a cylinder?
[tex]V = π {r}^{2} h[/tex]
where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant approximately equal to 3.14.
4) Given, radius =3.8 m and height = 8 m
Substituting the given values into the formula, we get:
[tex]V = π × (3.8)^2 × 8 \\ V = 115.52\pi \: cubic \: meters[/tex]
Therefore, the volume of the cylinder is approximately 361.984 cubic meters.
5) Given, radius = 5 in and height = 14 in
Substituting the given values:
[tex]V = π(5²)(14) \\ V = π(25)(14) \\ V = 350π[/tex]
Therefore, the volume of the cylinder is 350π cubic in (or approximately 1099.56 cubic meters if you want to use a numerical approximation for π).
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The combined City / Highway fuel economy of a 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range of 21mpg to 26mpg ANSWER BOTH A AND B
a sample size of at least 73 is needed to estimate the mean of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas with 98% confidence and an error of 0.25 mpg.
How to solve questions?
A. To estimate the standard deviation of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas, we can use the empirical rule for normal distribution. The empirical rule states that for a normally distributed random variable, about 68% of the values fall within one standard deviation of the mean, about 95% of the values fall within two standard deviations of the mean, and about 99.7% of the values fall within three standard deviations of the mean.
The range of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is 21 mpg to 26 mpg. We can estimate the mean by taking the average of the range:
Mean = (21 + 26) / 2 = 23.5 mpg
We can estimate the standard deviation by using the empirical rule. Since we know that about 68% of the values fall within one standard deviation of the mean, we can estimate the standard deviation as half the range that covers about 68% of the values:
Standard Deviation ≈ (26 - 21) / 4 = 1.25 mpg
B. To find the sample size needed to estimate the mean with 98% confidence and an error of 0.25 mpg, we can use the formula for the sample size:
n = (zα/2 * σ / E)²
where:
n is the sample size
zα/2 is the z-score corresponding to the desired confidence level, which is 2.33 for 98% confidence (from the standard normal distribution table)
σ is the population standard deviation, which we estimated in part A to be 1.25 mpg
E is the desired margin of error, which is 0.25 mpg
Substituting the values, we get:
n = (2.33 * 1.25 / 0.25)²
n = 72.96
Since we cannot have a fraction of a person in our sample, we round up to the next integer and get:
n = 73
Therefore, a sample size of at least 73 is needed to estimate the mean of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas with 98% confidence and an error of 0.25 mpg.
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The mystery number is a three-digit number. Its digits are 1, 8, and 6.
• The 8 has a digit on its left and on its right.
• The 6 is not the last digit.
What is the mystery number?
Answer:
a
Step-by-step explanation:
Amy is single with a salary of $50,000. She has been offered a new position that will raise her salary to $53,000.
The cut-off between the 18% and 25% tax brackets is $51,250. How much will her tax liability increase if she accepts the new position?
Please help ASAP! Thank you
Answer:
a. lines intersecting at a single point
b. one solution
Step-by-step explanation:
a. The equations can be rewritten as:
y = -5x+23 and y = -1/6x+1
Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.
Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.
b. The equation will have one solution as below.
The equations can be rewritten as:
5x+y=23
5x+30y=30
Subtracting both equation will result in,
29y=7
=> y=7/29
Hence x= 660/29
What does it mean to the rise over run when the slope is an integer? a. the rise number is one c. the run part of the slope is going to be one b. the run number is always negative d. there will be no slope Please select the best answer from the choices provided
When the slope is an integer the best answer would be a. the rise number is one.
What is integer?Any number, including zero, positive numbers, and negative numbers, is an integer. An integer can never be a fraction, a decimal, or a percent, it should be observed. Integers include things like 1, 3, 4, 8, 99, 108, -43, -556, etc.
When the slope is an integer, it means that the rise over run is also an integer, and the rise and run are relatively prime. Therefore, the best answer would be:
Therefore, the correct answer is a. the rise number is one.
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Mary Lou Mason purchased baby bottles for $4.56, baby formula for $12.45, and a pacifier for $2.13. For all purchases she must pay the state sales tax of 6.5 percent and the county tax of 1.5 percent. What is the tax on her purchases? Show all of your work.
Mary Lou Mason's total taxes on her purchase would be $1.37.
What are taxes?Taxes are mandatory payments to the government that are used to fund public services such as infrastructure, education, and health care. Taxes can be direct, such as income taxes, or indirect, such as sales taxes.
Mary Lou Mason's total purchase was $19.14.
To calculate the total taxes for her purchase, we can use the following formula:
Tax = (State Sales Tax %) x (Total Purchase) + (County Tax %) x (Total Purchase)
Therefore, the total taxes for Mary Lou Mason's purchase would be:
Tax = (6.5%) x ($19.14) + (1.5%) x ($19.14)
Tax = (0.065 x 19.14) + (0.015 x 19.14)
Tax = 1.24 + 0.13
Tax = $1.37
Mary Lou Mason's total taxes on her purchase would be $1.37.
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Antonio ahorra en el banco 10000 soles dicho banco le ofrece pagar una tasa de interés anual del 16% convertible mensualmente¿ Cuál será la tasa efectiva que recibe Antonio?
It's important to note that the effective interest rate takes into account the Compounding effect, which means that Antonio's savings will grow faster than if the interest was only applied annually.
Antonio has saved 10,000 soles in the bank, and the bank is offering him an annual interest rate of 16% which is compounded monthly. To find out the effective interest rate that Antonio will receive, we need to calculate the annual percentage yield (APY).
The formula for APY is (1 + (interest rate/number of compounding periods))^number of compounding periods - 1.
In this case, the interest rate is 16% and the number of compounding periods is 12 (since the interest is compounded monthly). Plugging these values into the formula, we get:
APY = (1 + (0.16/12))^12 - 1
APY = 0.1728 or 17.28%
So, the effective interest rate that Antonio will receive is 17.28%. This means that at the end of the year, he will have earned 1,728 soles in interest (assuming he doesn't withdraw any money from the account). It's important to note that the effective interest rate takes into account the compounding effect, which means that Antonio's savings will grow faster than if the interest was only applied annually.
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Lamont works at an electronics store where he receives a commission on his sales. He must choose between two plans for his pay structure for the next year.
For Plan A Lamont's monthly salary is $1,775 and he gets a 19% commission on his monthly sales. For Plan B his monthly salary is $2,100 and he gets a 7% commision on his monthly sales.
Use a system of equations to model Lamont's situation and choose the best response below.
If Lamont's sales are more than $2708.33, Plan A is a better plan because he earns more money in one month.
1. If Lamont's sales are $2708.33, he earns $2292.43 with Plan A.
2. If Lamont's sales are $2708.33, he earns $2290.63 with Plan B.
3. If Lamont's sales are more than $2708.33, Plan B is a better plan because he earns more money in one month.
4. If Lamont's sales are exactly $2,709.28, he earns the same amount of money with either plan.
The correct answer is option 2: if Lamont's sales are $2708.33, he earns $2290.63 with Plan B.
To determine which pay structure is better for Lamont, we need to compare the total amount of money he earns under each plan for different levels of sales. We can set up a system of equations to represent the two plans:
Plan A:
Total Pay = 1775 + 0.19S
where S is Lamont's total monthly sales
Plan B:
Total Pay = 2100 + 0.07S
To find the point at which the two plans yield the same result, we can set the two equations equal to each other and solve for S:
1775 + 0.19S = 2100 + 0.07S
0.12S = 325
S = 2708.33
If Lamont's monthly sales are exactly $2,708.33, then he earns the same amount of money under both plans - this is the break-even point.
However, for sales above this amount, Plan A becomes the better option as the commission rate is higher. Option 1 is incorrect because it assumes that Plan A is always better, whereas we know from the calculations that this is not the case. Option 3 is correct for sales above $2,708.33, but not for sales below this amount. Option 4 is also incorrect as we know that Plan B yields a slightly higher payout for sales exactly equal to the break-even point.
Therefore, option 2 is the correct answer as it accounts for the break-even point and accurately reflects the difference in total pay between Plan A and Plan B for Lamont's sales of $2,708.33.
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Becky recorded data for shoe size from 5 students: 3, 4.5, 4, 5, 4. Are the data an example of numerical data? Explain.
Answer:
Yes, the data is an example of numerical data.
1. This is about data, which means information that we can measure and count.
2. There are two types of numerical data: continuous and discrete.
3. Continuous numbers CAN have fractions, like 3.5, 4.2, or 5.0. 4. like show sizes
4. Discrete data CANNOT have fraction. only whole numbers, like 0, 1, 2, 3, and so on. like number of students in a class
7. "range" formula used to find the difference between discrete & continuous numerical data
8. "range" formula is largest value minus smallest value
Step-by-step explanation:
chatgpt
Answer: yes because it records the shoe sizes and you can calculate average, median, mode and range from this
Step-by-step explanation:
pls help me i need an answer
The first statement given is not a random sample because athletes leaving practice are not representative of all athletes.
"Athletes leaving practice are asked what their favorite sport is". Is this sampling a random sample or not?A random sample is a sample in which every member of the population being studied has an equal chance of being selected. In the given statement, the sample is not random because the athletes leaving practice are not representative of all athletes, as they may have different preferences or levels of skill in their favorite sport.
Additionally, the sample is not chosen through a random selection process, but rather through a convenience sampling method, in which participants are chosen based on their availability and willingness to participate.
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proof class in college: how proove 1+1=2 and not 11
We can give the proof to class with certainty that 1+1=2 and not 11.
What is proof and theorem?A statement that has been shown to be true based on a collection of axioms or presumptions is known as a theorem. This fact can be used to support other claims using mathematics. On the other hand, a proof is a logical argument that shows a theorem or claim to be true. In other terms, a proof is the procedure used to demonstrate a theorem's validity. A theorem may be true even in the absence of a proof, but it is not regarded as established until a proof is provided.
The basic properties of arithmetic can be used to prove 1 + 1 = 2.
The symbol "+" represents addition, thus 1 + 1 represents addition of 1 with 1 which is 2.
For 11 the 1 needs to be different place values which is not possible for 1 + 1.
Hence, we can give the proof to class with certainty that 1+1=2 and not 11.
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In which quadrant is the point (7, -2) located on the coordinate plane?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
SHOW YOUR WORK PLEASE.
Which graph is sequenced by definition by the function F(x)=3(2)x-1
Answer: Slope: 6y-intercept:(0,−1)
x= 0,1
y= -1,5
Step-by-step explanation:
Complete the Proof.
Given: ∠EAD ≅ ∠EBC; AD- ≅ BC-
Prove: CE- ≅ DE-
STATEMENTS
1. ∠EAD ≅ ∠EBC
2. ∠AEB ≅ ∠AEB
3. AD- ≅ BC-
4. ∆AED ≅ ∆BEC
5. CE- ≅ DE-
REASONS
1. Given
2. ___
3. Given
4. AAS
5. ___
1. ∠EAD ≅ ∠EBC (Given) 2. ∠AEB ≅ ∠AEB (Common angle) 3. AD- ≅ BC- (Given) 4. ∆AED ≅ ∆BEC (AAS) 5. CE- ≅ DE- (CPCT)
What is CPCT?According to the concept of corresponding parts of congruent triangles, or cpct, corresponding sides and corresponding angles of two congruent triangles are identical. The corresponding sides and angles of two triangles that are congruent to one another according to any of the following principles of congruency must be equal. When the corresponding sides and corresponding angles of two triangles are the same, two triangles are said to be congruent.
In the given figure given that, ∠EAD ≅ ∠EBC; AD- ≅ BC.
Thus,
1. ∠EAD ≅ ∠EBC (Given)
2. ∠AEB ≅ ∠AEB (Common angle)
3. AD- ≅ BC- (Given)
4. ∆AED ≅ ∆BEC (AAS)
5. CE- ≅ DE- (CPCT)
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please help quick its due by 11 am
Each of the value of x in the diagram above are as follows
x = 141 degreesx = 39 degreesx = 21 degreesx = 88 degreesx = 98 degreesx = 139 degreesx = 63 degreesx = 102 degreesx = 50 degreesx = 166 degreesx = 36 degreesx = 74 degreesx = 83 degreesx = 95 degreesx = 162 degreesWhat are corresponding angles?In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.
Next, we would determine each of the missing angles denoted by x as follows with respect to the START BOX;
x = 141° (alternate interior angles theorem).
x = 39° (corresponding angles).
x + 169 = 180
x = 180 - 169 = 21°.
x = 88° (vertically opposite angles).
x = 180°- 82°
x = 98°
x + 41 = 180
x = 180 - 41 = 139°.
x + 117 = 180
x = 180 - 117 = 139°.
x = 102° (vertically opposite angles)
x + 130 = 180
x = 180 - 130 = 50°.
x + 14 = 180
x = 180 - 14 = 166°.
x + 18 = 180
x = 180 - 18 = 162°.
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What is the width of a calculator?!!
Use properties of logarithms with the given approximations to evaluate the expression.
log 3≈ 0.477 and log 5≈ 0.699. Use one or both of these values to evaluate log 27.
log27=
The value of log(27) is 1.431.
What is logarithm?
The power to which a number must be raised in order to obtain other numbers is referred to as a logarithm. The easiest method to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms.
We can use the property of logarithms that states that log a (b^c) = c log a (b) to evaluate log 27 using the given approximations:
log 27 = log (3³) = 3 log 3 ≈ 3(0.477) ≈ 1.431
Therefore, log 27 ≈ 1.431.
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Draw a model to find a fraction equivalent to 1/4 show your work
A model to find a fraction equivalent to 1/4 is found to be 0.25.
Explain about the fraction:The intervals among two integers are illustrated by the display of fractions on a number line, which also reveals the basic idea behind the generation of fractional numbers.
The fractions on even a number line can be shown by splitting a whole into equal pieces, ranging from 0 to 1. The fraction's denominator would correspond to the number of equally spaced divisions that will be marked on the number line. To depict 1/8 on a number line, for instance, we would mark 0 and 1 on the two ends then divide that number line into 8 equal segments. The first interval can thus be designated as 1/8.Now, for the given fraction 1/4.
To get the model of 1/4, draw number line and mark number starting from
0 to 4.
Divide in 4 equal part.
The first part shows the fraction 1/4 = 0.25.
Thus, a model to find a fraction equivalent to 1/4 is found to be 0.25.
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How can you eliminate the x-terms in this system?
Answer:
3 times the second equation, plus the first
Step-by-step explanation:
You want a strategy for eliminating x-terms in the system of equations ...
9x -7y = -3-3x +5y = 9EliminationYou can eliminate x-terms by making their coefficients opposites. We observe that the coefficient of x in the first equation is -3 times the coefficient of x in the second equation.
Multiplying the second equation by 3 will make the x-coefficient -9, the opposite of that in the first equation. Doing that makes the system ...
9x -7y = -3-9x +15y = 27Adding these two equations together will eliminate the x-terms:
(9x -7y) +(-9x +15y) = (-3) +(27)
8y = 24 . . . . . . . simplify; x-terms are gone
You can eliminate x-terms by multiplying the second equation by 3, then adding the two equations together.
Please help!!
I don’t understand how to solve this since it’s format confuses me
Can someone explain how to answer it has to be a whole number or fraction.
Write as a single logarithm:
log 5 + 2
There is no logarithm base provided in the expression "log 5 + 2". Therefore, we assume that the base is 10, which is the default base for logarithms when no base is specified.
Using the logarithmic identity that states
"log a + log b = log(ab)",
we can combine the terms as follows:
log 5 + 2 = log(5) + log(10^2) [Note that 10^2 = 100]
Now, using the same identity, we can simplify this further:
log(5) + log(100) = log(5 * 100) = log(500)
Therefore, the expression "log 5 + 2" can be simplified as a single logarithm of "log 500" with base 10.
The bearing of F from A is 232°.
What is the bearing of A from F?
Hint: remember that co-interior angles sum to 180°.
The bearing from A to F is 38
Help find the area of these shapes I need 5 and 6!
Answer:
5) 120.3
6) 57
Step-by-step explanation:
5)9x8=72(area)
π(4)²=50.3(area)
total area= 72+50.3=120.3
6) 12x4=48(area)
7-4=3
12-9=3
3x3=9(area)
total area = 48+9=57
You are a new parent and would like to have $100,000 saved for your child’s college
education 18 years from now.
a. How much would you need to invest each year, starting now, to reach your goal
assuming 5% continuous annual interest?
b. What is the present value of that $100,000 when your child is born?
a. You would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000
b. The present value of $100,000 when your child is born is $100,000.
What is Compound Interest?Compound interest is interest that is calculated on the initial principal and also on the accumulated interest of previous periods. This results in exponential growth of the investment over time.
a. To calculate the amount that needs to be invested each year, we can use the formula for the future value of an annuity:
[tex]FV = PMT*((1 + r)^n - 1)/r[/tex]
where FV is the future value, PMT is the annual payment, r is the interest rate per period (which is 5% in this case), and n is the number of periods (which is 18 years).
Plugging in the values, we get:
$100,000 = PMT*((1 + 0.05)^18 - 1)/0.05
Solving for PMT, we get:
PMT = $3,436.76
Therefore, you would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000 for your child's college education in 18 years, assuming continuous compounding at a 5% annual interest rate.
b. To calculate the present value of $100,000 when your child is born, we need to discount it back to the present time using the formula:[tex]PV = FV/(1 + r)^n[/tex]
where PV is the present value, FV is the future value ($100,000), r is the interest rate per period (which is 5%), and n is the number of periods (which is 0 since the money is being received now).
Plugging in the values, we get:
PV = $100,000/(1 + 0.05)^0
Solving for PV, we get:
PV = $100,000
Therefore, the present value of $100,000 when your child is born is $100,000.
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A LITTER OF STAIN COVERS 100 SQUARES HOW MANY FEET LITTER SHOULD YOU BUY TO STAIN THE WHEEL CHAIR RAMP?
You would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.
Dimensional analysisThe answer to this question depends on the dimensions of the wheelchair ramp and how much area needs to be covered with stain.
Assuming that the wheelchair ramp has an area of 100 square feet, and that the stain coverage is similar to the area covered by paint, then the amount of stain required can be estimated by using the following formula:
Amount of stain (in liters) = Area to be covered (in square feet) ÷ Coverage per liter (in square feet per liter)
If the stain coverage is 25 square feet per liter, then the amount of stain required to cover 100 square feet would be:
Amount of stain = 100 ÷ 25 = 4 liters
Therefore, you would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.
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K
At a computer store, a customer is considering 8 different computers, 7 different monitors,
9 different printers and 2 different scanners. Assuming that each of the components is
compatible with one another and that one of each is to be selected, determine the number
of different computer systems possible.
there are 1,008 different computer systems possible, given the constraints provided.
what is constraints?
Constraints are limitations or conditions that must be satisfied in order to solve a problem or make a decision. In other words, constraints are rules or restrictions that define the boundaries within which a solution or decision must be made.
In the given question,
To determine the number of different computer systems possible, we need to multiply the number of choices for each component. This is based on the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.
So, for this problem, we have:
8 different choices for computers
7 different choices for monitors
9 different choices for printers
2 different choices for scanners
Using the multiplication principle, the total number of different computer systems possible is:
8 x 7 x 9 x 2 = 1,008
Therefore, there are 1,008 different computer systems possible, given the constraints provided.
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solve 3k-81ksquare=0
Answer:
k=0 or k=1/27
Step-by-step explanation:
3k-81k^2=0
3k(1-27k) =0
3k=0 or 1-27k=0
k=0 or -27k= -1
k= 1/27
There are three possible cases (or scenarios) for how many solutions that an absolute value equation could have. How many solutions are there for each case? Why are their differences in the number of solutions? Give a mathematical example in your explanation.
There are three possible cases for the number of solutions to an absolute value equation:
One solution: In this case, the absolute value of the expression equals a positive number. For example, the equation |x - 3| = 5 has one solution: x = 8 or x = -2.
Two solutions: In this case, the absolute value of the expression equals zero. For example, the equation |x - 3| = 0 has two solutions: x = 3.
No solution: In this case, the absolute value of the expression equals a negative number. However, the absolute value of any expression is always non-negative, so there can be no solutions. For example, the equation |x - 3| = -2 has no solutions.
The reason why there are differences in the number of solutions is because the absolute value function takes any input and returns a non-negative output. When we set an absolute value expression equal to a number, we are essentially splitting the equation into two parts: one where the expression is positive, and one where it is negative. Depending on the value that the absolute value expression is set equal to, we may get only one of these two parts (the positive part), both of them (the zero part), or none of them (the negative part).
For example, let's consider the absolute value equation |2x - 6| = 4. To solve this equation, we can split it into two cases:
Case 1: 2x - 6 = 4. Solving for "x", we get x = 5.
Case 2: -(2x - 6) = 4. Simplifying, we get -2x + 6 = 4, which gives us x = 1.
Therefore, the equation has two solutions: x = 1 and x = 5.
Answer:
Absolute value equations can have three possible cases based on the value within the absolute value brackets:
One solution: If the value within the absolute value brackets equals zero, there is only one solution. For example, |x| = 0 has the solution x = 0.
Two solutions: If the value within the absolute value brackets is positive, there are two solutions: one positive and one negative. For example, |x| = 3 has two solutions: x = 3 and x = -3.
No solutions: If the value within the absolute value brackets is negative, there are no solutions. For example, |x| = -2 has no solution because the absolute value of any real number is non-negative.
The differences in the number of solutions depend on the nature of the equation and the value within the absolute value brackets. If the value within the absolute value brackets equals zero, there is only one solution; if it is positive, there are two solutions; and if it is negative, there are no solutions.
For example, consider the absolute value equation |x - 5| = 7. If we subtract 5 from both sides, we get |x - 5| - 5 = 7 - 5, which simplifies to |x - 5| = 2.
Since the value within the absolute value brackets is positive, we know that there are two solutions. We can solve for both solutions by setting x - 5 equal to 2 and -2:
x - 5 = 2 => x = 7 x - 5 = -2 => x = 3
Therefore, the solutions to the absolute value equation |x - 5| = 7 are x = 3 and x = 7.
So to summarize, the number of solutions for an absolute value equation depends on the value within the absolute value brackets and can be one, two or zero, depending on the nature of the equation.
The graph shows two linear equations y = 2x + 1 and y = -3x - 4. Write the coordinates of the solution. (___ , ___)
y= 2x+1 y = -3x-4
2x-y+1 = 0. 3x+y+4 = 0
a1 + b1 + c1 = 0 a2+ b2 + c2 = 0
x,y = b1c2- b2c1/ a1b2-a2b1 , a2c1-a1c2/a1b2-a2b1
x,y = -1×4 - 1×1 /2×1 - 3×-1 , 3×1-2×4 / 2×1 -3×-1
x,y = -5/-1 , -5/2
x,y= 5, 5/2
Consider a triangle A BC like the one below. Suppose that a = 21, b = 26, and A = 349. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or"
The angles of the triangle are A=146.8°,B=22.3° and C=10.9°
define cosine ruleThe cosine rule states that for any triangle with sides of length a, b, and c and angles A, B, and C (with the side opposite each angle labeled with the corresponding lowercase letter), the following equation holds:
a² = b² + c²- 2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
Using the cosine rule,
a²=b²+c²-2bcCosA
2bcCosA=b²+c²-a²
A=cos⁻¹(b²+c²-a²/2bc)
A=cos⁻¹(18²+9²-26²/2×18×9)
A=cos⁻¹(-0.83642)=146.8°
Also from b²=a²+c²-2acCosB
B=cos⁻¹(a²+c²-b²/2ac)
B=cos⁻¹(26²+9²-18²/2×26×9)
B=cos⁻¹(0.925)=22.3°
The total angle of the triangle is 180°
A+B+C=180°
C=180°-146.8°+22.3°=10.9°
Thus, the angles of the triangle are A=146.8°,B=22.3° and C=10.9°
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